I've seen lots of pictures of 1910s/1920s touring cars but I don't know that I've seen one in person- maybe that would answer the question. They seem long enough to easily have three rows of seats, but they generally just have the front and rear seats. Why were they so long? The people in the back must have had enough room to sit on the floor and have a picnic or a poker game.
(I do know from my grandmother that her father used a modified touring car as an ambulance in the 1920s and 1930s, but I'm guessing that was the exception and, as mentioned, it was modified.)

Long wheelbases (the distance between the axles) made for a smoother ride on the rough roads of the day and you got a longer car to accommodate the longer wheelbase. Most engines of the time were also inline engines with at least four or sometimes six or eight cylinders in a row. This meant that you needed a longer hood to cover the engine. Finally, style probably paid a big role.

For comparison an Austin 20 has a length of 5100 mm while a Subaru Outback, a modern four door station wagon, is 4800 mm. A difference of a bit over one foot. The Austin is certainly a big car, but maybe not as big as it looks. The wheelbases are very long as well, helped by the front wheels being set a long way forward.

The smooth running characteristics of the straight-8 made it popular in luxury and racing cars of the past. However, the engine's length demanded the use of a long engine compartment, making the basic design unacceptable in modern vehicles. Also, due to the length of the engine, torsional vibration in both crankshaft and camshaft can adversely affect reliability and performance at high speeds. In particular, a phenomenon referred to as "crankshaft whip," caused by the effects of centrifugal force on the crank throws at high engine rpm, could cause physical contact between the connecting rods and crankcase walls, leading to the engine's destruction. As a result, the design has been displaced almost completely by the shorter V8 engine configuration.

They don't seem to have much storage area behind the rear seat. So I'm guessing they carried the luggage inside the passenger compartment, behind the driver's seat?

They had a fold-out rack at the rear of the car, above the bumper, that when folded down could have a truck (hence "trunk") strapped to it.
As far as the interior, there were often jump seats tucked up behind the front seats that could be pulled out and would face the rear seats.

This one passes through a few steps to get to its modern sense. We start with:

Boot, the (usually leather) garment that cover the foot and lower leg, which gives us:

Boot, a piece of armour which cover the foot or lower leg or both, which gives us:

Boot, protective metal gear attached to stirrups or stirrup harnesses to protect the rider's foot or lower leg but which was also useful in mounting and demounting, which gives us:

Boot, a metal bracket or (later) step on the outside of a coach, used when getting in and out, which give us:

Boot, a larger platform on the (out)side of a coach or carriage where an attendant would sit, usually facing outwards (i.e. sideways). When the coach stopped the attendant would jump down, open the door and assist his social betters out of the coach. This gives us:

Boot, a platform at the front or back of a coach or carriage where attendants sat or (more usually) luggage was strapped, which when enclosed gives us:

Long wheelbases (the distance between the axles) made for a smoother ride on the rough roads of the day and you got a longer car to accommodate the longer wheelbase. Most engines of the time were also inline engines with at least four or sometimes six or eight cylinders in a row. This meant that you needed a longer hood to cover the engine. Finally, style probably paid a big role.

I don't know why you think that these cars have too much sitting space. I think it's the contrary : we've become accustomed to have a too small sitting space. Sitting in a modern car isn't easy and straighforward (you don't sit in the back of a car the way you would, say, sit on your couch). You have to bend your legs, possibly push away the front seat, you can't move naturally your legs while sitted nor extend them....The sitting space isn't spacious at all. It's as narrow as it can be without sitting becoming plainly uncomfortable.

I find pretty normal that people back them wanted a sitting space where they would feel at ease.

ST's vBulletin 3 Responsive Styles

Our newly refreshed styles in 2017, brings the old vb3 to the new level, responsive and modern feel. It comes with 3 colors with or without sidebar, fixed sized or fluid. Default vbulletin 3 style made responsive also available in the pack.
Purchase Our Style Pack Now